Hydrodynamics of a class of $N$-urn linear systems

Abstract

In this paper we are concerned with hydrodynamics of a class of Nurn linear systems, which include voter models, pair-symmetric exclusion processes and binary contact path processes on N urns as special cases. We show that the hydrodynamic limit of our process is driven by a (C[0, 1]) ′ -valued linear ordinary differential equation and the fluctuation of our process, i.e, central limit theorem from the hydrodynamic limit, is driven by a (C[0, 1]) ′ -valued Ornstein-Uhlenbeck process. To derive above main results, we need several replacement lemmas. An extension in linear systems of Chapman-Kolmogorov equation plays key role in proofs of these replacement lemmas.